The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 aX aX X (a+1)X (a+1)X X
0 0 X 0 0 (a+1)X X 0 aX aX aX X aX
0 0 0 X 0 X (a+1)X (a+1)X aX 0 aX X 0
0 0 0 0 X (a+1)X aX X (a+1)X X 0 X (a+1)X
generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+84x^28+165x^32+180x^36+3072x^39+240x^40+204x^44+138x^48+12x^52
The gray image is a linear code over GF(4) with n=52, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0206 seconds.